Math // Multiplication & Division

Multiplying and dividing

Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
1 code

Quick check

Can the learner quickly work out '4.7 × 100' or '3,600 ÷ 1,000' — knowing that digits shift left or right in the place-value chart depending on whether they're multiplying or dividing?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Calculate 3.45 × 100 = 345
  • Calculate 72 ÷ 1000 = 0.072
  • Explain that multiplying by 10 shifts each digit one place to the left

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

2 topics
  • Dividing by 10 and 100Required

    Fractions // Ages 8 to 9

    Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals

  • Place Value × 10 PatternRequired

    Number Representation & Place Value // Ages 9 to 10

    ×10 place-value relationship is prerequisite to ×÷ by powers of 10

You are here

Multiplying and dividing

Ages 9 to 10 // Method

Leads to

3 topics

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For ages 9–10: multiply and divide whole numbers and decimals by 10, 100 and 1000 by understanding that each digit SHIFTS across the place-value columns — digits move left for multiplying and right for dividing, while the decimal point stays fixed. This replaces the fragile 'add a zero' rule, which breaks for decimals (3.45×100 is 345, not 3.4500), and the memorised 'move the point' rule, which gives the same numerical result but hides why the value changes and is easily misapplied (for example where to put the point in a whole number, or forgetting placeholder zeros). The skill underpins metric conversions and powers-of-ten notation.

Common misconceptions

  • 'Add a zero' rule misapplied to decimals (3.45×100 wrongly written as 3.4500).
  • 'Move the decimal point' causing confusion about direction or number of places.
  • Shifting the wrong number of places for the power of ten.
  • Forgetting to fill empty places with zeros as placeholders when needed (e.g. 72÷1000 = 0.072).
  • Thinking dividing always makes the digits smaller in value without understanding the place shift.

Useful representations

  • Place-value / Gattegno chart with sliding digits (point fixed)
  • Arrow/shift diagram showing 1/2/3 places for 10/100/1000
  • Decimal place-value columns (tenths, hundredths, thousandths)
  • Metric conversion tables as an application

Teaching practices

  • Teach as a digit SHIFT across place-value columns (digits move left for ×, right for ÷), not 'add a zero' or 'move the point', which mislead with decimals.
  • Use a place-value/Gattegno chart where digits physically slide the correct number of places, with the decimal point fixed.
  • Introduce tenths/hundredths/thousandths through ÷10/100/1000 so the columns to the right of the point are meaningful.
  • Link the number of places to the power of ten (×1000 → 3 places) and later to exponent notation.
  • Connect to metric conversions (m↔cm↔mm, kg↔g) as an authentic application.

Activities to try

  1. 1

    Sliding digits on a place-value chart

    Why it works: Multiplying or dividing by a power of ten changes what each digit is worth, so the digits shift the matching number of place-value columns; the decimal point does not move, and empty columns must be filled with placeholder zeros.

    1. Set up a place-value chart with labelled columns from hundreds down to thousandths (… H T O • t h th) and a fixed decimal point.
    2. Place 3.45 in the columns, then multiply by 100: slide every digit TWO columns to the LEFT so the 3, 4 and 5 become 345. Note that nothing was appended — the digits moved.
    3. Now test the tempting 'just add two zeros' shortcut on 3.45 and compare: it gives 3.4500, which is wrong. Discuss why the shortcut fails for decimals.
    4. Divide 72 by 1000: slide every digit THREE columns to the RIGHT, and fill each empty column it crosses with a placeholder zero, giving 0.072 (including the leading 0).
    5. Compute 6 × 10 by sliding one place left (giving 60), and connect the number of places shifted to the number of zeros in 10/100/1000 (×1000 → 3 places).
  2. 2

    Reference chart with reveal-able shift arrows

    Why it works: A clear reference links each power of ten to a fixed number of places and direction, reinforcing that the direction and count — not zero-appending — determine the result.

    1. Study a place-value chart annotated with arrows that show the shift for ×10 (one place), ×100 (two places) and ×1000 (three places), and the reverse for division.
    2. Answer the prompt 'why isn't 3.45 × 100 = 3.4500?' and check your reasoning against a revealed explanation.
    3. State in your own words how many places each power of ten shifts the digits and in which direction.
  3. 3

    Spot-the-error and fill-in consolidation

    Why it works: Consolidation surfaces the specific decimal trap (3.4500) and the placeholder-zero requirement (0.072), confirming whether digit-shift reasoning is secure rather than a fragile trick.

    1. Complete 72 ÷ 1000 = ___ , writing all placeholder zeros.
    2. Choose the correct value of 3.45 × 100 from options including the trap value 3.4500, and explain why the trap is wrong.
    3. Find and fix the mistake in a worked example where a digit has been shifted the wrong number of places.
    4. Explain, for one of your answers, how the value of each digit changed.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/2.3g

Math // Multiplication & Division

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